Fix Laplacian calculation in spectral partitioning #2568
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Also partially answers #379, though we may want additional testing beyond what is provided here. |
In the previous implementation of spectral partitioning, the eigenvalue computation was actually performed on the original adjacency matrix, not the graph Laplacian thereof. This change provides a utility for computing the graph Laplacian, which is then fed into the new implementation of the Lanczos solver. An additional test is provided to ensure that the end-to-end spectral partitioning quality is as expected.
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These changes enable the use of the new Lanczos solver for spectral partitioning. This solver gives the correct eigenvalues in some cases where the old solver did not, but a previous attempt to introduce this led to a downstream breakage because the Laplacian was not being calculated correctly in the spectral partitioning logic.
In this PR, we introduce a new
compute_graph_laplacianfunction to correctly generate a new CSR matrix representing the graph Laplacian of the input CSR-formatted adjacency matrix. This resolves #2419. This function is used in the spectral partition function to obtain the correct partitioning using the new Lanczos solver. This eliminates all internal uses ofcomputeSmallestEigenvectors, the old Lanczos implementation, which should allow it to be removed after a deprecation cycle for downstream consumers. This will in turn allow us to resolve #313.Note that the originally-reported breakage from the previous attempt to switch to the new Lanczos solver was used to create the test confirming correct functionality of the current PR.
This PR is marked as a bugfix because it unblocks usage of the corrected Lanczos implementation. It is based on and requires PR #2541, and it will be marked as draft until that PR is merged.